# Many-Body Scars from Floquet Automata
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**Anchor paper:** K. Agarwal, P.G. Rozon, M.J. Gullans, "Constructing quantum many-body scar Hamiltonians from Floquet automata," *Phys. Rev. B* 106, 184304 (2022). [arXiv:2112.12153]
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## Background
Quantum many-body scars are rare, non-thermalizing eigenstates violating the eigenstate thermalization hypothesis, best known through the PXP model (Rydberg-atom chains), where special initial states show anomalous periodic revivals. Separately, quantum cellular automata / Floquet automaton circuits are a class of exactly solvable driven systems built from local permutation gates, whose brickwork structure makes revivals exactly trackable. It was unclear how to bridge these: automaton circuits give exact revivals but are discrete and fine-tuned, while realistic scar models like PXP are static Hamiltonians with only approximate, decaying revivals — no general recipe connected the two.
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## New results
The authors give a systematic method for turning two-layer Floquet automaton circuits into static quantum many-body scar Hamiltonians, imposing a hierarchy of local commutation rules ("Type I"/"Type II") that force local gates to commute increasingly well within a chosen orbit (scar) subspace. When satisfied, a controlled Baker-Campbell-Hausdorff expansion extracts an effective time-independent Hamiltonian whose dynamics reproduces the automaton's revivals over a long prethermal window before eventually decaying — naturally explaining the finite revival timescales seen in real scarred systems. The construction recovers the celebrated PXP model itself as a special case, and generates new scar-model families (QMBS-A/B/C).
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![Quantum cellular automaton commutation rules](https://arxiv.org/html/2112.12153v2/Figure_RulesIllustration.png)
*Fig. 1 — a quantum cellular automaton converting one Néel state to another (a), and the local Type I/Type II and global commutation rules enforced on the orbit subspace (b-d).*
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## Related work in this direction
- P.G. Rozon, K. Agarwal, "Broken unitary picture of dynamics in quantum many-body scars," Phys. Rev. Research 6, 023041 (2024) — reinterprets the same scarred Hamiltonians via operators that fail to commute globally but do commute within the scar subspace, an alternative, more general explanation for the revivals.
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# Parents
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* Driven/Floquet Localization & Symmetry Engineering⏎